The dynamics of fluctuations is considered for electrons near a positive ion
or for charges in a confining trap. The stationary nonuniform equilibrium
densities are discussed and contrasted. The linear response function for small
perturbations of this nonuniform state is calculated from a linear Markov
kinetic theory whose generator for the dynamics is exact in the short time
limit. The kinetic equation is solved in terms of an effective mean field
single particle dynamics determined by the local density and dynamical
screening by a dielectric function for the non-uniform system. The
autocorrelation function for the total force on the charges is discussed.Comment: 4 pages, 1 figure. Results presented at the "International Conference
on Strongly Coupled Coulomb Systems", Camerino, Italy, July 2008. Submitted
for publication in the conference proceedings (special issue of Journal of
Physics A
